We used CMIP6 GCMs to quantify climate change impacts on precipitation and potential evapotranspiration (PET) across water management zones (WMZs) in Uganda. Future changes are assessed based on four Shared Socioeconomic Pathways (SSP) scenarios including SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 over the periods 2021–2040, 2041–2060, 2061–2080, and 2081–2100. Both precipitation and PET are generally projected to increase across all the WMZs. Annual PET in the 2030s, 2050s, 2070s, 2090s will increase in the ranges 1.1–4.0%, 4.8–7.9%, 5.1–11.8%, and 5.3–17.1%, respectively. For the respective periods, annual precipitation will increase in the ranges 4.0–7.8%, 7.8–12.5%, 7.9–19.9%, and 6.9–26.3%. The lower and upper limits of these change ranges for both precipitation and PET are, respectively, derived under SSP1-2.6 and SSP5-8.5 scenarios. Climate change will impact on PET or precipitation disproportionately across the WMZs. While the eastern WMZ (Kyoga) will experience the largest projected precipitation increase especially towards the end of the century, the southern WMZ (Victoria) exhibited the largest PET increase. Our findings are relevant for understanding hydrological impacts of climate change across Uganda, in the background of global warming. Thus, the water sector should devise and implement adaptation measures to impede future socioeconomic and environmental crises in the country.